JEE MAIN - Physics (2022 - 28th July Morning Shift - No. 7)
Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $$2 v$$.
In the light of the above statements, choose the correct answer from the options given below :
Both Statement I and Statement II are true
Both Statement I and Statement II are false
Statement I is true but Statement II is false
Statement I is false but Statement II is true
Explanation
Average momentum $$ = \left\langle {\overrightarrow P } \right\rangle = 0$$
$${v_{rms}} = \sqrt {{{3RT} \over M}} $$
If temperature is doubled and oxygen atoms are used then
$$v{'_{rms}} = \sqrt {{{3R(2T)} \over {M/2}}} = 4\,{v_{rms}}$$
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